The advantage of measuring the dilution factor is that the ensuing coating loss estimation is then exclusively based on measured quantities: sample loss angle, mode frequency and mass. Therefore, unlike other experimental setups based on the ring-down method, our method does not require prior knowledge of coating Young modulus and thickness. Furthermore, one can estimate coating Young modulus \(Y\)  and Poisson ratio \(\nu \)  by fitting the results of finite-element simulations to measured values of \(D\)  estimated via Eq. (REF ). Compared to nano-indentation, such method does not rely on the prior knowledge of \(\nu \) , and does not depend on the nature of the substrate used nor on the model chosen for data analysis [1]}. Figure REF  shows best-fit results for three mode families of different shapes and frequency [1]}, giving \(Y = 120 \pm 3\)  GPa and \(\nu = 0.32 \pm 0.01\) . Details about our fitting method and finite-element simulations can be found elsewhere [1]}, [4]}.
